Sally Dowler described her joyful reaction when she was able to reach her daughter's voicemail, which she thought indicated she might be alive and checking her messages.

Messages from her phone had apparently been deleted by private detective Glenn Mulcaire, working for the News of the World.

"I rang her phone and it clicked through on to her voicemail and I just jumped and said: 'She's picked up her voicemails Bob, she's alive'," Dowler said, raising her voice as she remembered the moment.

"When we heard about the hacking that was the first thing I thought ... I told my friends, 'she's picked up her voicemail, she's picked up her voicemail'."

Dowler also spoke about how she first found out that her daughter's phone was hacked during Levi Bellfield's trial for her murder, and said that she didn't sleep for three nights after learning the news.

"It was terribly difficult to process it," she said. "What do you do with that information in your mind?"

The Dowlers also described their anger when photos of a private retracing of their daughter's last steps appeared in a newspaper.

Sally Dowler said she was "really cross" when the photographs were published in the News of the World.

The couple also described their meeting with News Corporation chairman Rupert Murdoch after the phone hacking scandal was reported by the Guardian newspaper.

"It was a very tense meeting," Sally Dowler said. "He was very sincere."

Bob Dowler said that the newspapers should reconsider the way they obtain and publish stories in light of the hacking scandal.

"Given the gravity of what became public domain knowledge," he said. "One would sincerely hope that News International and other media organisations would look very carefully at how they procure and obtain information about stories as obviously the ramifications are far greater than just the story in the press."

Inquiry chairman Lord Justice Leveson thanked the Dowlers for agreeing to give evidence and paid tribute to their loss.

"Can I thank you both for being prepared to come to the inquiry," he said. "You have done so voluntarily and I am very conscious that it is a strain.

"I can only sympathise with both of you for the appalling losses that you have suffered and for the traumas that you have undergone over many years."

Prime Minister David Cameron set up the inquiry in July after it emerged that the Sunday tabloid commissioned private detective Glenn Mulcaire to hack the schoolgirl's phone after she disappeared in 2002.

As well as listening to Milly's voicemails, the investigator also erased some of them to make room for new messages, falsely leading her family to believe she was still alive, the inquiry was told.

David Sherborne, counsel for the Dowlers and other victims of press intrusion, told the inquiry last week that Mrs Dowler felt "euphoria" when she finally got through to her missing daughter's voicemail as a result of Mulcaire's deletions.

"Perhaps there are no words which can adequately describe how despicable this act was," he said.

Mulcaire was jailed along with the News of the World's former royal editor, Clive Goodman, in January 2007 after they admitted intercepting voicemail messages left on phones belonging to royal aides.